Dynamical Characteristic Analysis And Synchronization For A New Hyperchaotic System

Chaos is a unique phenomenon in nonlinear systems with complex dynamics,and chaos theory is an important branch of modern nonlinear systems.A new hyperchaotic system was constructed based on the Lü system by adding a nonlinear state feedback controller.The dynamical characteristics such as dissipation,equilibrium point stability,and initial value sensitivity of the system were analyzed.By analysing the Lyapunov exponent of the system,the range of system parameters and the corresponding phase diagrams were derived for the system in periodic,quasi-periodic,chaotic and hyperchaotic states.The circuit topology and component parameters were derived from the system's equation.The circuit schematic was designed and the circuit simulation was carried out by Multisim software.The hardware circuit of the system was implemented according to the circuit schematic,and the phase diagram in each state of the system was observed by the oscilloscope.This thesis is the first time to use the cosine similarity method to compare the hardware circuit test results of the system with the MATLAB simulation results.The results show that the hardware circuit test results are highly consistent with the MATLAB simulation results when the system in the periodic,quasi-periodic,chaotic and hyperchaotic states,which illustrates the accuracy of the hardware circuit implementation of the system.The thesis also investigated the synchronization control of the system,realising the self-synchronization and different structure synchronization of the system,and completed the hardware circuit,the test results show the feasibility of synchronization systems,which provides a reference for its application in secure communications.